Question: Simplify the following expression: $ y = \dfrac{-3}{5} + \dfrac{-3}{4a + 9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4a + 9}{4a + 9}$ $ \dfrac{-3}{5} \times \dfrac{4a + 9}{4a + 9} = \dfrac{-12a - 27}{20a + 45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-3}{4a + 9} \times \dfrac{5}{5} = \dfrac{-15}{20a + 45} $ Therefore $ y = \dfrac{-12a - 27}{20a + 45} + \dfrac{-15}{20a + 45} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{-12a - 27 - 15}{20a + 45} $ $y = \dfrac{-12a - 42}{20a + 45}$